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The dot-depth hierarchy of star-free languages is infinite. (English) Zbl 0368.68074


MSC:

68Q45 Formal languages and automata
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References:

[1] Brzozowsm, J. A., Hierarchies of aperiodic languages, Rev. Française d’Automatique Informat. Recherche Operationnelle Série Rouge (Informatique Théorique), 10, 35-49 (1976)
[2] Brzozowski, J. A.; Culík, K.; Gabrielian, A., Classification of noncounting events, J. Comput. System Sci., 5, 41-53 (1971) · Zbl 0241.94050
[3] Cohen, R. S.; Brzozowski, J. A., Dot-depth of star-free events, J. Comput. System Sci., 5, 1-16 (1971) · Zbl 0217.29602
[4] McNaughton, R.; Papert, S., Counter-Free Automata (1971), M.I.T. Press: M.I.T. Press Cambridge, Mass · Zbl 0232.94024
[5] Schutzenberger, M. P., On finite monoids having only trivial subgroups, Inform. Contr., 8, 190-194 (1965) · Zbl 0131.02001
[6] Simon, I., Piecewise testable events, (Lecture Notes in Computer Science 33 (1975), Springer-Verlag: Springer-Verlag New York) · Zbl 0316.68034
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